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A Thesis Submitted for the Degree of PhD at the University of Warwick Permanent WRAP URL: http://wrap.warwick.ac.uk/108066 Copyright and reuse: This thesis is made available online and is protected by original copyright. Please scroll down to view the document itself. Please refer to the repository record for this item for information to help you to cite it. Our policy information is available from the repository home page. For more information, please contact the WRAP Team at: [email protected] warwick.ac.uk/lib-publications IEDDED CODING ALGORITHMS APPLICABLE TO TIME VARIABLE CHANNELS By: Farshid Zolghadr, B.Sc., AMIEE A thesis presented for the degree of Doctor of Philosophy in the Department of Engineering, University of Warwick November 1989 THE BRITISH LIBRARY DOCUMENT SUPPLY CENTRE BRITISH THESES NOTICE The quality of this reproduction is heavily dependent upon the quality of the original thesis submitted for microfilming. 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LS23 7BQ United Kingdom TABLE OF CONTENTS TITLE PAGE CONTENTS i LIST OF TABLES AND ILLUSTRATIONS V ACKNOWLEDGEMENTS x DECLARATIONS xi ABSTRACT x^v CHAPTER 1 : INTRODUCTION 1 CHAPTER 2 : THEORETICAL BACKGROUND 6 2.1 Source Coding (theory) 6 2.1.1 Discrete Sources 6 2.1.2 Huffman Coding 9 2.1.3 Run-Length Codes 10 2.1.4 T-codes: Methods of Code Construction 11 2.2 Channel Models (theory) 17 2.2.1 Discrete Memoryless Channels 17 2.2.2 Channels with Memory 20 2.3 Channel Coding (theory) 22 2.3.1 Block Codes 22 2.3.2 Decoding of Linear Block Codes 24 2.3.3 Convolutional Codes 26 2.3.4 Decoding of Binary Convolutional Codes 30 2.3.5 Soft Decision Decoding 31 2.4 Modems for Time Variable Channels 34 2.4.1 Modulation Methods 34 2.4.2 Demodulation Methods 36 i CHAPTER 3 : REAL TIME CHANNEL EVALUATION 41 3.1 Introduction 41 3.2 Statistical Real Time Channel Evaluation (SRTCE) 44 3.2.1 SRTCE System 44 3.2.2 Use of T-codes in an SRTCE System 50 3.2.3 SRTCE in the Presence of AWGN 53 3.2.4 SRTCE for the Gilbert-Elliot Channel 55 3.3 Performance Study of SRTCE System 58 3.3.1 AWGN Channel 58 3.3.2 The Gilbert-Elliot Channel 61 3.4 Discussions 63 CHAPTER 4 : EMBEDDED BLOCK ENCODING 65 4.1 Introduction 65 4.2 Embedded Array Codes 66 4.2.1 Code Structure 69 4.2.2 Performance Analysis 70 4.2.3 Results 80 4.3 Modified Embedded Array Code 85 4.3.1 Performance Analysis 86 4.4 Discussions 88 CHAPTER 5 : EMBEDDED CONVOLUTIONAL ENCODING 90 5.1 Introduction 90 5.2 Embedded Convolutional Encoding 93 5.2.1 The Overall System 94 5.2.2 ARQ Format 99 5.3 Main System Elements in Detail 101 5.3.1 The Encoder 101 ii 5.3.2 The Channel 103 5.3.3 Metric Evaluator 104 5.3.4 Soft Decision Decoder 105 5.3.5 Real Time Channel Evaluation 108 System (Error Limiter) 5.4 Performance Study 113 5.5 Discussions 1 i5 CHAPTER 6 : MULTIPLE FREQUENCY SHIFT KEYING MODEM 118 6 .1 Introduction 11 g 6.2 Overview of Some Common Synchronisation Methods 120 6.3 Principles of the CABS System 123 6.4 Implementation of the CABS Modem 135 6.4.1 Modulator Design Philosophy 135 6.4.2 Demodulator Design and Implementation 140 6.5 Results of Simulation and On-Line Testing 144 of the Modem 6.5.1 Simulation Results 145 6.5.2 Modem Operation Verification 146 6.5.3 AWGN Channel Test Results 148 6.5.4 HF Trials Test Results 150 6.6 Discussions 153 CHAPTER 7 : CONCLUSIONS A SUGGESTIONS FOR FURTHER WORK 155 7 .1 Conclusions 155 7.1.1 Statistical RTCE 155 7.1.2 Embedded Block Encoding Techniques 156 7.1.3 Embedded Convolutional Encoding 156 7.1.4 MFSK Modem Algorithms 157 iii 7.2 Further Work 158 7.2.1 Extensions of Multi-Functional Coding 158 7.2.2 Improvement of the Embedded Encoding 1 59 7.2.3 Embedded Convolutional Code Under 159 CABS Environment 7.2.4 Improvements of the CABS Modem 160 7.2.5 Extensions of the CABS Modem 161 7.2.6 Semi-Orthogonal MFSK Modulation Format 161 REFERENCES 164 SYMBOLS AND ABBREVIATIONS 176 APPENDIX A : ERROR PROBABILITY OF PARTIAL ARRAY CODE 180 APPENDIX B : ERROR PROBABILITY OF EMBEDDED ARRAY CODE 182 APPENDIX C : PERFORMANCE ANALYSIS OF THE OUTER DECODER 185 APPENDIX D : PERFORMANCE ANALYSIS OF (52.36) ARRAY CODE IN 189 AN ARQ SYSTEM APPENDIX E : MODULATOR PROGRAM LISTING 191 APPENDIX F : DEMODULATOR PROGRAM LISTING 196 iv LIST or TABLES AND ILLUSTRATIONS Tig.2.1 Example text and its equivalent encoded 15 data stream. Fig.2.2 Example of automatic synchronisation of 16 T-code, S{ 1,3,7,15,10,6,8}. Fig.2.3 Two state model of a memoryless channel. 18 Fig. 2.4 Gilbert's model. 20 Fig. 2.5 Convolutional Encoder for v»3, m=2, b=1. 27 Fig.2.6 Tree-code representation of encoder of 28 Tig.2.5. Fig.2.7 Trellis diagram of encoder of Fig.2.5 29 Fig.3.1 2-state model, M1, of binary source. 45 Fig.3.2 Codeword length distribution of the 53 (1,3,7,15,10,6,8) T-code. Fig.3.3 The conditional pdf of baseband signal 54 (♦1, -1) in presence of AWGN with standard deviation of 0.6. Fig.3.4 The Gilbert-Elliot channel model. 56 Fig.3.5 Effect of buffer size N and the actual 60 channel BER on the rms error in BER estimated, for AWGN Channel. Fig.3.6 rms error in estimation vs buffer size, 62 Gilbert Elliot channel, channel BER = 0.0508. Fig.4.1 ARQ Protocol of the Embedded Encoding Scheme. 66 Fig. 4.2 Embedded Encoding Block Structure. 67 Fig.4.3 Generalised Embedded Array Code Block 69 Structure. Fig.4.4 Shortened (52,12) Array Code. 70 Fig.4.5 Embedded Array Code, Decoder structure. 72 Fig.4.6 Block Diagram of 'Super channel'. 72 Fig.4.7 Possible Decoding Paths. 74 Fig.4.8 Required Number of Repeat Requests for 75 Decoding a Given Sub-Block. Fig.4.9 Decoding Paths and Their Probabilities. 76 Fig.4.10 Probability Tree for Embedded Array Code. 79 Fig.4.11 (52,12) Embedded Array Code Block Structure. 80 Fig.4.12 Theoretical Throughput of array and Embedded 83 Array Codes under AWGN Channel Conditions. Fig.4.13 Theoretical Reliabilities of Array and 83 Embedded Array Codes under AWGN Channel Conditions. Fig.4.14 Simulated Throughput of Array and Embedded 84 Array Codes under AWGN Channel Conditions. Fig.4.15 Simulated Reliability of Array and Embedded 84 Array Codes under AWGN Channel Conditions. Fig.4.16 Modified Embedded Encoding Scheme. 85 Fig.4.17 (64,23) Modified Embedded Array Code Block 86 Structure. Fig.4.18 Simulated Throughput under AWGN Channel for 87 (52,12) Embedded Code and (64,23) Modified Embedded Array Code. Fig.4.19 Simulated reliability under AWGN Channel 87 for (52,12) Embedded Code and (64,23) Modified Embedded Array Code. Fig.5.1 ARQ Protocol of the Embedded Convolutional 91 Code. Fig.5.2 Embedded Convolutional Encoded Block Structure. 91 Vi Fig.5.3 System Block Diagram. 94 Fig.5.4 Convolutional Encoder for 133<«>, 171,., Code. 95 Fig.5.5 Metric Assignment for Soft Decision Data. 99 Fig.5.6 Trellis Diagram for 7<«>, 5,., convolutional 106 code. Fig.5.7 pdf of the Error Detection Metrics for 110 Channel SNR«2dB, Rate«1/2. Fig.5.8 pdf of the Error Detection Metrics for 110 Channel SNR=3dB, Rate«1/2. Fig.5.9 pdf of the Error Detection Metrics for 111 Channel SNR«4dB, Rate-1/2. Fig.5.10 Mean and Standard Deviation of the Error 111 Detection Metrics vs Channel SNR (dB). Fig.5.11 Output BER vs Channel S/N (dB) for Code Rate 112 1/2, 2/3 and 3/4 Convolutional Code. Fig.5.12 Throughput of the Embedded Convolutional 114 and the Comparison Codes. Fig.5.13 Reliability of the Embedded Convolutional 114 and the Comparison Code. Fig.6.1 CABS Modulator Block Diagram. 124 Fig.6.2 CABS System Convolutional Encoder and 124 Trellis Diagram. Fig.6.3 Block Diagram of the Noncoherent Correlator. 125 Fig.6.4 Noncoherent Correlator outputs for Input 127 Tone Sequence 1, 4, 2, 3 and 2. Fig.6.5a pdf of the Correlator Output based on HypO, 131 T.»1 , E«1, o=0.1 with mean of Z « 1.02. Fig.6.5b pdf of the Correlator Output based on Hypl, 132 T„= 1, E= 1, o=0.1 with mean of Z = 0.02.